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1. Chapter 3- Logic Gates II PUC, MDRPUC, Hassan
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Chapter-3
LOGIC GATES
Introduction:
Gate: A Gate is a simply an electronic circuit which operates on one or more input signals and
always produces an output signal.
Gates are digital (two state) circuits because the input and output signals are either low voltage (0) or
high voltage (1).
Gates are often called logic circuits because they can be analyzed with Boolean algebra.
Gates are classified into two types:
Basic Gates:
NOT Gate:
A NOT gate has only one input and one output.
The output state is always the opposite of the input state.
A NOT Gate is also called as Inverter gate, because the output is not same as the input.
The output is sometimes called the complement (opposite) of the input.
The logical symbol and the truth table of NOT gate are given below.
X X
OR Gate:
A OR gate has two or more input signal but only one output signal.
If any of the input signals is 1 (high), then the output is 1 (high).
The logical symbol for two-input OR gate and the truth table is given below.
X
0 1
1 0
Logic gates
Basic Gates Derived Gates
AND OR NOR NAND XOR
NOT XNOR
2. Chapter 3- Logic Gates II PUC, MDRPUC, Hassan
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X F = X + Y
Y
AND Gate:
A AND gate has two or more input signal but only one output signal.
When all the input signals are 1 (high), the output is 1 (high), otherwise the output is 0.
The logical symbol for two-input AND gate and the truth table is given below.
X F = X .Y
Y
NOR Gate:
A NOR gate has two or more input signal but only one output signal.
The NOR gate is a complemented of OR gate.
The output of NOR gate will be 1 only when all inputs are 0 and output will be 0 if any input
represents a 1.
NOR is short form of NOT-OR.
The symbol is used to represent a NOR operation. So X + Y can be written as X NOR Y or X Y.
The logical structure shows an OR gate and NOT gate. For input X and Y, the output of the OR gate
will be X+Y which is fed as input to the NOT gate. So the output of NOR gate is given by X + Y
which is equal to X . Y
X F = X + Y F = X + Y
Y
The logical symbol for two-input NOR gate and the truth table is given below.
X F = X + Y
Y
X Y F = X+Y
0 0 0
0 1 1
1 0 1
1 1 1
X Y F = X.Y
0 0 0
0 1 0
1 0 0
1 1 1
X Y Z F = + +
0 0 0 1
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 0
X Y F = +
0 0 1
0 1 0
1 0 0
1 1 0
3. Chapter 3- Logic Gates II PUC, MDRPUC, Hassan
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NAND Gate:
A NAND gate has two or more input signal but only one output signal.
The NAND gate is a complemented of AND gate.
The output of NAND gate will be 0 only when all inputs are 1 and output will be 0 if any input
represents a 0.
NAND is short form of NOT-AND.
The symbol is used to represent a NOR operation. So X . Y can be written as X NAND Y or X Y.
The logical structure shows an AND gate and NOT gate. For input X and Y, the output of the OR
gate will be X .Y which is fed as input to the NOT gate. So the output of NAND gate is given by
X . Y which is equal to X + Y
X F = X . Y F = X . Y
Y
The logical symbol for two-input NAND gate and the truth table is given below.
X F = X . Y
Y
XOR (Exclusive-OR) Gate:
An exclusive-OR has two or more input signal but only one output signal.
Exclusive-OR gate is different form of OR gate.
Exclusive-OR gate produces output 1 for only those input combinations that have odd number of 1’s.
The output is 0 if there are even number of 1’s in the input.
The output is 1 if there are odd number of 1’s in the input.
In Boolean algebra, ϴ sign stands for XOR operation. Thus X XOR Y can be written as XϴY
If the output is given by:
F = X ϴ Y
X Y F = .
0 0 1
0 1 1
1 0 1
1 1 0
X Y Z F = . .
0 0 0 1
0 0 1 1
0 1 0 1
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0
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F = X Y + X Y
The XOR gate has a symbol similar to OR gate, except the additional curved line of the input side.
X F = X ϴ Y = X Y + X Y
Y
The following truth table illustrates XOR operation for 2 and 3 inputs.
XNOR (Exclusive-NOR) Gate:
The XNOR gate is complement of XOR gate.
The output of XNOR is 1 only when the logic values of both X and Y is same i.e. either both are
equal to 1 or both are 0.
Its output is 0 when its inputs are different.
In Boolean algebra, ʘ sign stands for XNOR operation. Thus X XNOR Y can be written as X ʘ Y
If the output is given by:
F = X ʘ Y
F = XY + XY
The XNOR gate has a symbol similar to NOR gate, except the additional curved line of the input side.
X F = X ʘ Y = XY + X Y
Y
The following truth table illustrates XOR operation for 2 and 3 inputs.
Number
Of 1’s
Input Output
X Y F = X ϴ Y
EVEN 0 0 0
ODD 0 1 1
ODD 1 0 1
EVEN 1 1 0
Number
of 1’s
X Y Z F = X ϴ Y ϴ Z
EVEN 0 0 0 0
ODD 0 0 1 1
ODD 0 1 0 1
EVEN 0 1 1 0
ODD 1 0 0 1
EVEN 1 0 1 0
EVEN 1 1 0 0
ODD 1 1 1 1
Number
Of 1’s
Input Output
X Y F = X ʘ Y
EVEN 0 0 1
ODD 0 1 0
ODD 1 0 0
EVEN 1 1 1
Number
of 1’s
X Y Z F = X ʘ Y ʘ Z
EVEN 0 0 0 1
ODD 0 0 1 0
ODD 0 1 0 0
EVEN 0 1 1 1
ODD 1 0 0 0
EVEN 1 0 1 1
EVEN 1 1 0 1
ODD 1 1 1 0
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Universal Gate (NAND & NOR):
Universal gate is a gate using which all the basic gates can be designed.
NAND and NOR gate re called as Universal Gates, because all the Boolean functions can also be
implemented using these two gates.
NAND and NOR gates are more popular as these are less expensive and easier to design.
Realization of all basic gates using NAND gate:
NAND to NOT:
In the figure we have two input NAND gate whose inputs are purposely connected together so that
the same input is applied to both.
F = X . X = X
X
From the diagram X NAND X = X . X
= X + X // DeMorgan’s 2nd
Theorem
= X X + X = X
= Inverted Input = NOT gate
NAND to AND:
In the figure we have two NAND gates connected so that the AND operations is performed.
NAND gate 2 is used as a NOT gate.
X F1 = X . Y F2 = X. Y = X.Y
Y
From the diagram X NAND Y =F1= X . Y
F2 = F1 . F1
= F1 + F1 // DeMorgan’s 2nd
Theorem
= X. Y X + X = X
F2 = X.Y
= AND gate
NAND to OR:
The OR operation can be implemented using NAND gates connected as shown in figure.
NAND gate 1 and NAND gate 2 are used as NOT to invert the inputs.
F1 = X
X
F3 = X . Y = X + Y
F2 = Y
Y
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From the diagram X NAND Y
F1 = X . X = X + X = X
F2 = Y . Y = Y + Y = Y
F3 = F1 . F2
= F1 + F2 // DeMorgan’s 2nd
Theorem
= X + Y X = X and Y = Y
F3 = X +Y
= OR gate
Realization of all basic gates using NOR gate:
NOR to NOT:
Figure shows that NOR gate with its inputs connected together behaves as a NOT gate.
F = X + X = X
X
From the diagram X NOR X = X + X
= X . X // DeMorgan’s 1st
Theorem
= X X . X = X
= Inverted Input = NOT gate
NOR to AND:
The AND operation can be implemented with NOR gate as shown in figure. Here NOR gate 1 and
NOR gate 2 are used as NOT gate to invert inputs.
F1 = X
X
F3= X + Y = X.Y
F2 = Y
Y
From the diagram X NOR Y
F1 = X + X = X . X =X
F2 = Y + Y = Y . Y =Y
F3 = F1 + F2
= F1 . F2 // DeMorgan’s 1st
Theorem
= X . Y X = X and Y = Y
F3 = X.Y
= AND gate
7. Chapter 3- Logic Gates II PUC, MDRPUC, Hassan
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NAND to OR:
In the figure two NOR gates are arranged so that the OR operation is performed.
NOR gate 2 is used as NOT gate.
X F1 = X + Y F2 = X + Y = X + Y
Y
From the diagram X NOR Y
F1 = X + Y
F2 = F1 + F1
F2 = F1 . F1 // DeMorgan’s 1st
Theorem
= F1
= X + Y X = X
F2 = X +Y
= OR gate
Designing of Logic Circuit using all basic gates :
Designing of Logic Circuit using NAND and NOR gates:
CHAPTER – LOGIC GATES BLUE PRINT
VSA (1 marks) LA (3 Marks) - Total
01 Question 01 Question - 02 Questions
Question No 1 Question No 20 - 04 Marks
